Bond graph modelling of hydraulic six-degree-of-freedom motion simulator

Stewart-type six-degree-of-freedom motion simulator is a multidisciplinary system containing multiple mechanical, hydraulic and electric components. This article proposed a unified bond graph representation for the simulator. First, dynamics equations of the upper platform are developed using Newton-Euler method and its bond graph model is established. Each hydraulic actuator is then modelled according to the three basic equations of valve-controlled cylinder. An equivalent approach is further employed to treat the inertial effects of each cylinder. This approach projects the forces caused by the cylinder inertia equivalently onto the joint point of the upper platform, which relatively simplifies the modelling of the piston and the tube. The whole simulator takes independent close-loop position feedback control on each valve-controlled cylinder actuator. A proportional controller with dynamic pressure feedback and feed-forward compensation is proposed. The bond graph model of the overall simulator is finally completed with 20-Sim software, and further simulations and experiments are carried out to verify the model. The model provides another reference for motion simulator modelling besides the multibond graph approach.